Ben Ish Hai S"B Yito 11 permits people to walk on snow on Shabbat. [Also, later on he discusses if you allowed to mush snow into a cup of water to make it cold, and prohibits it (as well as S"A O"H 320- and Alex's answer). ]

Shulhan Aruch (ibid.) prohibits the crushing of ice, however, permits the placing of it in a cup to make things cold (also see for lengthy discussion the aforementioned BI"H and later on in that Parasha).